Publications

When we perform probabilistic inferences with the Gaia Mission data, we technically require a likelihood function, or a probability of the (raw-ish) data as a function of stellar (astrometric and photometric) properties. Unfortunately, we aren't (at present) given access to the Gaia data directly; we are only given a Catalog of derived astrometric properties for the stars. How do we perform probabilistic inferences in this context? The answer - implicit in many publications - is that we should look at the Gaia Catalog as containing the parameters of a likelihood function, or a probability of the Gaia data, conditioned on stellar properties, evaluated at the location of the data. Concretely, my recommendation is to assume (for, say, the parallax) that the Catalog-reported value and uncertainty are the mean and root-variance of a Gaussian function that can stand in for the true likelihood function. This is the implicit assumption in most Gaia literature to date; my only goal here is to make the assumption explicit. Certain technical choices by the Mission team slightly invalidate this assumption for DR1 (TGAS), but not seriously. Generalizing beyond Gaia, it is important to downstream users of any Catalog products that they deliver likelihood information about the fundamental data; this is a challenge for the probabilistic catalogs of the future.

When we perform probabilistic inferences with the Gaia Mission data, we technically require a likelihood function, or a probability of the (raw-ish) data as a function of stellar (astrometric and photometric) properties. Unfortunately, we aren't (at present) given access to the Gaia data directly; we are only given a Catalog of derived astrometric properties for the stars. How do we perform probabilistic inferences in this context? The answer - implicit in many publications - is that we should look at the Gaia Catalog as containing the parameters of a likelihood function, or a probability of the Gaia data, conditioned on stellar properties, evaluated at the location of the data. Concretely, my recommendation is to assume (for, say, the parallax) that the Catalog-reported value and uncertainty are the mean and root-variance of a Gaussian function that can stand in for the true likelihood function. This is the implicit assumption in most Gaia literature to date; my only goal here is to make the assumption explicit. Certain technical choices by the Mission team slightly invalidate this assumption for DR1 (TGAS), but not seriously. Generalizing beyond Gaia, it is important to downstream users of any Catalog products that they deliver likelihood information about the fundamental data; this is a challenge for the probabilistic catalogs of the future.

Cold stellar streams---produced by tidal disruptions of clusters---are long-lived, coherent dynamical features in the halo of the Milky Way. Due to their different ages and different positions in phase space, different streams tell us different things about the Galaxy. Here we employ a Cramer--Rao (CRLB) or Fisher-matrix approach to understand the quantitative information content in eleven known streams (ATLAS, GD-1, Hermus, Kwando, Orinoco, PS1A, PS1C, PS1D, PS1E, Sangarius and Triangulum). This approach depends on a generative model, which we have developed previously, and which permits calculation of derivatives of predicted stream properties with respect to Galaxy and stream parameters. We find that in simple analytic models of the Milky Way, streams on eccentric orbits contain the most information about the halo shape. For each stream, there are near-degeneracies between dark-matter-halo properties and parameters of the bulge, the disk, and the stream progenitor, but simultaneous fitting of multiple streams will constrain all parameters at the percent level. At this precision, simulated dark matter halos deviate from simple analytic parametrizations, so we add an expansion of basis functions to give the gravitational potential more freedom. As freedom increases, the information about the halo reduces overall, and it becomes more localized to the current position of the stream. In the limit of high model freedom, a stellar stream appears to measure the local acceleration at its current position; this motivates thinking about future non-parametric approaches. The CRLB formalism also permits us to assess the value of future measurements of stellar velocities, distances, and proper motions. We show that kinematic measurements of stream stars are essential for producing competitive constraints on the distribution of dark matter, which bodes well for stream studies in the age of Gaia.

We compute the electronic Green’s function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green’s function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.

The wide-band limit is a commonly used approximation to analyze transport through nanoscale devices. In this work we investigate its applicability to the study of charge and heat transport through molecular break junctions exposed to voltage biases and temperature gradients. We find that while this approximation faithfully describes the long-time charge and heat transport, it fails to characterize the short-time behavior of the junction. In particular, we find that the charge current flowing through the device shows a discontinuity when a temperature gradient is applied, while the energy flow is discontinuous when a voltage bias is switched on and even diverges when the junction is exposed to both a temperature gradient and a voltage bias. We provide an explanation for this pathological behavior and propose two possible solutions to this problem.

Compressing large data sets to a manageable number of summaries that are informative about the underlying parameters vastly simplifies both frequentist and Bayesian inference. When only simulations are available, these summaries are typically chosen heuristically, so they may inadvertently miss important information. We introduce a simulation-based machine learning technique that trains artificial neural networks to find nonlinear functionals of data that maximize Fisher information: information maximizing neural networks (IMNNs). In test cases where the posterior can be derived exactly, likelihood-free inference based on automatically derived IMNN summaries produces nearly exact posteriors, showing that these summaries are good approximations to sufficient statistics. In a series of numerical examples of increasing complexity and astrophysical relevance we show that IMNNs are robustly capable of automatically finding optimal, nonlinear summaries of the data even in cases where linear compression fails: inferring the variance of Gaussian signal in the presence of noise, inferring cosmological parameters from mock simulations of the Lyman-α forest in quasar spectra, and inferring frequency-domain parameters from LISA-like detections of gravitational waveforms. In this final case, the IMNN summary outperforms linear data compression by avoiding the introduction of spurious likelihood maxima. We anticipate that the automatic physical inference method described in this paper will be essential to obtain both accurate and precise cosmological parameter estimates from complex and large astronomical data sets, including those from LSST and Euclid.

Multi-epoch radial velocity measurements of stars can be used to identify stellar, sub-stellar, and planetary-mass companions. Even a small number of observation epochs can be informative about companions, though there can be multiple qualitatively different orbital solutions that fit the data. We have custom-built a Monte Carlo sampler (The Joker) that delivers reliable (and often highly multi-modal) posterior samplings for companion orbital parameters given sparse radial-velocity data. Here we use The Joker to perform a search for companions to 96,231 red-giant stars observed in the APOGEE survey (DR14) with ≥3 spectroscopic epochs. We select stars with probable companions by making a cut on our posterior belief about the amplitude of the stellar radial-velocity variation induced by the orbit. We provide (1) a catalog of 320 companions for which the stellar companion properties can be confidently determined, (2) a catalog of 4,898 stars that likely have companions, but would require more observations to uniquely determine the orbital properties, and (3) posterior samplings for the full orbital parameters for all stars in the parent sample. We show the characteristics of systems with confidently determined companion properties and highlight interesting systems with candidate compact object companions.

Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks that could have benefits for near-term devices. The result is a unified framework where classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes where, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a optimization procedure that could be carried out on quantum hardware, and testing the noise resilience of the trained model.

We investigate the electronic structure of SrMnO3 with density functional theory plus dynamical mean-field theory (DMFT). Within this scheme the selection of the correlated subspace and the construction of the corresponding Wannier functions is a crucial step. Due to the crystal-field splitting of the Mn-3d orbitals and their separation from the O-2p bands, SrMnO3 is a material where on first sight a three-band d-only model should be sufficient. However, in the present work we demonstrate that the resulting spectrum is considerably influenced by the number of correlated orbitals and the number of bands included in the Wannier function construction. For example, in a d−dp model we observe a splitting of the t2g lower Hubbard band into a more complex spectral structure, not observable in d-only models. To illustrate these high-frequency differences we employ the recently developed fork tensor product state (FTPS) impurity solver, as it provides the necessary spectral resolution on the real-frequency axis. We find that the spectral structure of a five-band d−dp model is in good agreement with PES and XAS experiments. Our results demonstrate that the FTPS solver is capable of performing full five-band DMFT calculations directly on the real-frequency axis.